1. The functional model

Contents

1.1 Theoretical tides

Providing a high-resolution structure for Tide Generating Potential (TGP) constituents
- by identifying the main constituents of a wave group by their well-known Darwin symbols
- by identifying constituents derived from the Moon’s ascending node and perigee as well from annual modulations and supplying them with new symbol names up to 10 character in lengths.
- minor constituents with Darwin symbols are associated with a wave group and remain unchanged.
Implementation of this new structure for the TGPs of Hartmann, Wenzel 1995, Kudryavtsev 2003 and Tamura 1987.

In addition to the WDZ Earth model, the DDW-H and DDW-NHi Earth models are selectable for analysis.
Approximations of gravimetric and diminishing factors of potential degree 6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.
Approximations of Love and Shida numbers of potential degrees 4-6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.
Free core nutation modelling based on the supported Earth models for all tidal components including displacements and strains.
Alternatively using Earth model tidal parameters instead of adjusted parameters from a Least Squares analysis for calculating the observation residuals.

Generalizing the functional model by integrating constituents of degree 1 of the TGP.
Definition of reference potential functions Vij, i.e.
- V20, V21, V22, V33, V44, V55, V66
- the Vij are totally covering the tidal frequency domains and each Vij only containing constituents j of a certain potential degree i.

Definition of non-reference or satellite potential functions Vkj of different potential degrees l than the reference potential functions ( k .ne. i ) but possessing the same orders j so that they share the same frequency domains (e.g. V31 in V21, V32 in V22 etc.) :
- V10, V11
- V30, V31, V32
- V40, V41, V42, V43
- V50, V51, V52, V53, V54
- V60, V61, V62, V63, V64, V65
Hypothesis free grouping of tidal constituents by means of reference and satellite wave groups defined by degree-dependent option codes.
Provision of templates for optimal wave grouping suited for different observation lengths like > 18 years, 4 years, 1 year.
Provision of the quality criterion “Correlation RMSE Amplifier (CRA)” for assessing the optimal wave group model.

Pole and LOD tide information from
- “IERS EOP PC Observatoire de Paris”, (http://hpiers.obspm.fr/eop-pc/index.php?index=C04& lang=en), or from
- “The United States Naval Observatory (USNO) Washington”, ftp://maia.usno.navy.mil/ser7/finals2000A.all.
- No extra programs are needed due to TAI-UT1 being tabulated or evaluated.
Interpolation of daily pole and LOD tide data to hourly and minute samples by cubic splines with continuous conditions or Lagrange interpolation.
Reduction of the astronomical channels from the tidal observations by predefined reduction coefficients prior to a Least Squares analysis .

Modelling meteorological regression channels (e.g. station air pressure, ATMACS gravity ,etc.) by causal and/or non – causal impulse response functions of arbitrary lengths.
Estimating the associated frequency transfer functions yielding frequency-dependent regression coefficients and phase shifts.
Reduction of the meteorological channels (e.g. station air pressure, gravity due to attraction and loading of the atmosphere etc.) from the tidal observations by predefined reduction coefficients prior to a Least Squares analysis.

Uniform polynomial model over the complete tidal record with identical coefficients for all blocks.

Modelling of non-linear harmonics of tidal origin with known non-linear frequencies by an iterative feed-back analysis procedure.
Modelling of additional harmonics of tidal and/or non-tidal origin by an iterative feed-back analysis procedure.

Deployment of window functions in combination with the Least Squares technology for improving analysis design and interpretation.